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**Water shoots up from a fountainat a speed of v0 at a rate of dm/dt, and hits a garbage can of mass M suspended in the air. What is the maximum height the fountain can lift the garbage can?**

First i approached this problem with K.E = P.E

i assumed that m at time t = (dm/dt)t

so i put {M+(dm/dt)t}gh = 1/2 {(dm/dt)tv^2}

then i solved the equation for h.

i am not so sure if my approach is right...

Is there a better of solving this problem?